naginterfaces.library.matop.complex_​herm_​matrix_​exp

naginterfaces.library.matop.complex_herm_matrix_exp(uplo, a)[source]

complex_herm_matrix_exp computes the matrix exponential, , of a complex Hermitian matrix .

For full information please refer to the NAG Library document for f01fd

https://www.nag.com/numeric/nl/nagdoc_28.4/flhtml/f01/f01fdf.html

Parameters
uplostr, length 1

If , the upper triangle of the matrix is stored.

If , the lower triangle of the matrix is stored.

acomplex, array-like, shape

The Hermitian matrix .

Returns
acomplex, ndarray, shape

If no exception or warning is raised, the upper or lower triangular part of the matrix exponential, .

Raises
NagValueError
(errno )

An internal error occurred when computing the spectral factorization. Please contact NAG.

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: or .

(errno )

The computation of the spectral factorization failed to converge.

Notes

is computed using a spectral factorization of

where is the diagonal matrix whose diagonal elements, , are the eigenvalues of , and is a unitary matrix whose columns are the eigenvectors of . is then given by

where is the diagonal matrix whose th diagonal element is . See for example Section 4.5 of Higham (2008).

References

Higham, N J, 2005, The scaling and squaring method for the matrix exponential revisited, SIAM J. Matrix Anal. Appl. (26(4)), 1179–1193

Higham, N J, 2008, Functions of Matrices: Theory and Computation, SIAM, Philadelphia, PA, USA

Moler, C B and Van Loan, C F, 2003, Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later, SIAM Rev. (45), 3–49